Worst Singularities of Plane Curves of Given Degree

Plane Curves of Minimal Degree with Prescribed Singularities

We prove that there exists a positive α such that for any integer d ≥ 3 and any topological types S1, . . . , Sn of plane curve singularities, satisfying μ(S1) + · · ·+ μ(Sn) ≤ αd, there exists a reduced irreducible plane curve of degree d with exactly n singular points of types S1, . . . , Sn, respectively. This estimate is optimal with respect to the exponent of d. In particular, we prove tha...

Efficient Resolution of Singularities of Plane Curves

We give a new algorithm for resolving singularities of plane curves. The algorithm is polynomial time in the bit complexity model, does not require factorization, and works over Q or finite fields.

Deformations of Singularities of Plane Curves

In this paper we present some new results in the deformation theory of plane curve singularities. The methods rely on the study of analytic properties of linear non homogeneous ODE’s.

Eecient Resolution of Singularities of Plane Curves

We give a new algorithm for resolving singularities of plane curves. The algorithm is polynomial time in the bit complexity model, does not require factorization, and works over Q or nite elds.

Resolution of Singularities for Plane Curves